1. Technical Field of the Invention
The present invention relates to an optical filtering apparatus and method which perform optical filtering (spatial frequency filtering).
2. Description of the Prior Art
Optical filtering is a representative parallel optical computing technique. In this case, a Fourier spectrum of an input image is changed by using a spatial frequency filter.
Representative optical filtering techniques are low-pass filtering and high-pass filtering. Generally, low frequency components of an image spectrum correspond to a brief image structure, and edges and fine structure concentrate in a high frequency components. A low-pass filter passes only low frequency components, thus removing noise of high frequency components. A high-pass filter passes only high frequency components for the purpose of extracting image boundaries and enhancing the fine structure. Further, a band-pass filter which passes only a predetermined spatial frequency band is utilized in image compression and image analysis.
Conventionally, in optical filtering, a filter having a two-dimensional transmittance distribution is used as a spatial frequency filter.
FIG. 18 shows an example of the conventional optical filtering method. In this method, input image light 1 is Fourier-transformed by a lens 2. A filter 4 having a two-dimensional transmittance distribution is provided on a Fourier transform surface of the lens 2. A part of Fourier spectrum 3 Fourier transformed of the input image light 1 is passed through the filter 4, and a transmission spectrum 5 is Inverse-Fourier-transformed by a lens 6. Thus output image light 7 is obtained.
In low-pass filtering, the filter 4, as shown as a filter 4L in FIG. 19A, has a central round region corresponding to a low frequency spectrum of the Fourier-transformed image 3 as a light transmitting portion 4a, and the other region corresponding to a high frequency spectrum as a light shield portion 4b. Only the low frequency spectrum of the Fourier-transformed image 3 is passed through the filter 4.
In high-pass filtering, the filter 4, as shown as a filter 4H in FIG. 19B, has a central round region corresponding to a low frequency spectrum of the Fourier-transformed image 3 as a light shield portion 4c, and the other region corresponding to a high frequency spectrum as a light transmitting portion 4d. Only the high frequency spectrum of the Fourier-transformed image 3 is passed through the filter 4.
When the low-pass filtering and the high-pass filtering are simultaneously performed, as shown in FIG. 20, for example, the input image light 1 is divided into two light waves by a half mirror 8. Input image light 1L passed through the half mirror 8 is Fourier-transformed by a lens 2L, and a low frequency spectrum 5L of a Fourier-transformed image 3L passes through the filter 4L. The Fourier-transformed image 3L is Inverse-Fourier-transformed by a lens 6L. Thus the low frequency 7L is obtained. On the other hand, input image light 1H reflected by the half mirror 8 is further reflected by a mirror 9, and Fourier-transformed by a lens 2H. A high frequency spectrum 5H passes through the filter 4H, and Inverse-Fourier-transformed by a lens 6H. Thus the high frequency reconstructed image light 7H is obtained. The original input image can be reconstructed by combining the low frequency reconstructed image light 7L and the high frequency reconstructed image light 7H.
However, since the above-described conventional optical filtering method passes a predetermined frequency component and cuts other frequency components, the cut frequency components are lost on the filter output side. Accordingly, the original input image cannot be reconstructed.
That is, in a case where the filter 4 in FIG. 18 is a low-pass filter as the filter 4L in FIG. 19A, the high frequency spectrum of the Fourier-transformed image 3 is lost on the output side. On the other hand, in a case where the filter 4 is a high-pass filter as the filter 4H in FIG. 19B, the low frequency spectrum is lost on the output side.
Accordingly, in a case where the low-pass filtering and the high-pass filtering are simultaneously performed or in a case where an original input image is reconstructed, it is necessary to provide two filters 4L and 4H, two Fourier transform lenses and Inverse-Fourier transform lenses, and an optical system to divide the input image light 1 into two optical waves, as shown in FIG. 20. This complicates the filtering apparatus and increases the apparatus in size.
The present invention has been made in view of the above circumstances, and enables selective or simultaneous execution of mutually-complementary low-pass filtering and high-pass filtering and the like, by using a common medium, without losing respective frequency components of Fourier spectrum on the output side, further enables reconstruction of original input image with ease.
According to an aspect of the present invention, the optical filtering apparatus has: a birefringent medium that modulates polarization of a Fourier-transformed image passed therethrough, in accordance with a two-dimensional birefringent distribution, formed in accordance with a spatial frequency distribution of the Fourier-transformed image; and a polarization device provided in an optical path of light passed through the birefringent medium.
Further, according to another aspect of the present invention, the optical filtering method includes the steps of: passing a Fourier-transformed image of an input image through a birefringent medium where a two-dimensional birefringent distribution corresponding to a spatial frequency distribution of the Fourier-transformed image is formed, so as to modulate polarization of the Fourier-transformed image in accordance with the birefringent distribution; and extracting, by a polarization device analyzer, a polarized light component in a desired or predetermined orientation from light passed through the birefringent medium.
In accordance with the present invention as described above, as a filtering medium, a birefringent medium where a two-dimensional birefringent distribution is formed is used in place of a filter having a two-dimensional transmittance distribution. A spatial frequency filter is formed with the birefringent medium and a polarization device analyzer.
As the birefringent medium, an electrically addressed type spatial light modulator, an optical storage medium having an optical storage layer exhibiting photo-induced birefringence on at least one surface side, on which the two-dimensional birefringent distribution is recorded, or the like, can be used. As the polarization device, a analyzer (analyzer), a polarizing beam splitter or the like can be used.
For example, in a case where low-pass filtering and high-pass filtering are selectively or simultaneously performed, in the birefringent medium, the formed birefringent distribution has a central round region corresponding to a low frequency spectrum of Fourier-transformed image in an orientation of 45xc2x0 to a predetermined orientation (0xc2x0), and the other region corresponding to a high frequency spectrum is in the orientation of 0xc2x0.
In this arrangement, when the Fourier-transformed image 0xc2x0 polarized from an input image passes through the birefringent medium, the polarization of the low frequency spectrum is rotated 90xc2x0, to an orientation of 90xc2x0, while the polarization of the high frequency spectrum is not rotated, still in the orientation of 0xc2x0.
Accordingly, if an analyzer is provided in the optical path of light passed through the birefringent medium and the orientation of the analyzer is adjusted to 90xc2x0, only 90xc2x0 polarized component can be extracted through the analyzer. In this manner, the low-pass filtering is performed.
Further, the high-pass filtering is performed by adjusting the orientation of the same analyzer to 0xc2x0 so as to extract only 0xc2x0 polarized component of the light passed through the birefringent medium.
Further, if the orientation of the analyzer is adjusted to 45xc2x0, the 90xc2x0 and 0xc2x0 polarized components passed through the birefringent medium are simultaneously extracted via the analyzer, and the original input image can be reconstructed.
Further, if a polarization beam splitter is provided in the optical path of the light passed through the birefringent medium and the 90xc2x0 and 0xc2x0 polarized components of the light passed through the birefringent medium are extracted via the polarization beam splitter, the low-pass filtering and the high-pass filtering can be simultaneously performed. Further, the original input image can be reconstructed by combining the both output light obtained via the polarization beam splitter.
Further, filtering other than the low-pass filtering and the high-pass filtering such as band-pass filtering or band elimination can be performed by changing the two-dimensional birefringent distribution formed in the birefringent medium.
Other features and advantages of the present invention will be apparent from the following description taken in conjunction with the accompanying drawings, in which like reference characters designate the same name or similar parts throughout the figures thereof.